How do you find the average value of the function for #f(x)=1-x^4, -1<=x<=1#?

Answer 1

Ezekiel Alexander

The average value is #4/5#.

The average value is given by

#A = 1/(b - a) int_a^b f(x)dx#

Where #f(x)# is a continuous function on #[a, b]#.

#A = 1/(1 - (-1)) int 1 - x^4#

#A = 1/2[(x - 1/5x^5)]_-1^1#

#A = 1/2(1 - 1/5 - (-1 - 1/5(-1)^5))#

#A = 1/2(4/5 + 1 - 1/5)#

#A = 1/2(8/5)#

#A = 4/5#

Hopefully this helps!

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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How do you find the average value of the function for #f(x)=1-x^4, -1&lt;=x&lt;=1#?

How do you find the average value of the function for #f(x)=1-x^4, -1<=x<=1#?